Bayesian estimation _ mode_computation

[KKLS]

by jpfeifer » Tue Nov 29, 2016 8:53 pm

Not exactly. What you see in those two graphs is an example of bimodality, where the MCMC correctly explores both regions. You still might want to use a longer chain to properly sample from both modes. But there is nothing here to suggest that the chain has not yet converged to its ergodic distribution.
Have you looked at a trace_plot of the posterior density?

Yes I have. and I have included them in the zip folder that i attached.

There is small drift in the middle of the replications horizon for few of the parameters.
I will keep raising it though. Thanks.

One final question, : in the estimation command can i put all the options that go with stoch_simul (i.e order=1, hpfilter=1600, irf=40 ) ???

Many many thanks gain for your time Prof. Pfeifer.

[jpfeifer]

No, you included the trace_plot for the parameters, but not the one for the posterior density itself, i.e. the result from

No, you cannot put all the same options there. The manual tells you what is allowed. For example, the hp_filter does not work with estimation

[KKLS]

Hi Prof. Pfeifer and all ,
I tried several times to follow up on Prof. Pfeifer advise (see quote below) regarding the trace plot :

by jpfeifer » Wed Nov 30, 2016 10:36 am
No, you included the trace_plot for the parameters, but not the one for the posterior density itself, i.e. the result from
Code: Select all
trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,1)

so after the **estimation ** command i set these commands :

trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,1);
trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,2);

… but I was not able to get the trace plot . I am getting an error as below.

Estimation::mcmc: Posterior (dsge) IRFs…
Estimation::mcmc: Posterior IRFs, done!
Not enough input arguments.

Error in trace_plot (line 39)
column = name2index(options_, M_, estim_params_, type, name1);

Error in BggGKlinear (line 1250)
trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,1);

Error in dynare (line 180)
evalin(‘base’,fname) ;

Ps.
I tried only for block one,i.e:

trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,1);

… and I tried writing the command above after I had asked for trace plot of individual estimated parameters (and shocks)

trace_plot(options_,M_,estim_params_,‘StructuralShock’,2,‘epsA’);
…
all shocks and parameters
…

trace_plot(options_,M_,estim_params_,‘PosteriorDensity’,1);

I get the same error ( Dynare produces the trace plot for individual parameters but not the one for the posterior density) . Did I miss something pls ?

[jpfeifer]

That command only works in the unstable version of Dynare, to be released as Dynare 4.5.

[KKLS]

Hi to Prof. Pfeifer and all,

I have read the previous posts regarding the model comparisons via likelihoods ratio (and odds ratio) .

From one post of Prof. Pfeifer it seems that to compare to models estimated on different data sets , the odds ratio comparisons are not vaild (see the quote below) .

My question that follows is:
if I got two models A and B where one is a nested version of the other, and where

• for the smaller model I use a data series X and Y (plus some other data which are the same in the two models)
• for the bigger model I use a data series Z = X+Y (that is Z is the sum of X and Y).

The reason I do not use the extra data series on the smaller model is that the smaller model provides a variable which is counterpart to Z only (but no info on its components X or Y).

1. Can I still use the odds ratio comparison based on marginal densities (Laplace and ModifiedHarmonicMean) ?
2. Is there an alternative way of comparing these models ?

Many thanks again Profesor

Ps.

[quote]
Re: Model Comparison Bayesian Estimation (again)
Postby jpfeifer » Fri Apr 04, 2014 9:04 am
Basically all your answers are in Koop’s 2003 textbook “Bayesian Econometrics” on pages 4-5.

1. For Bayesian model comparison models do not need to be nested and there is a natural degrees of freedom correction. **Hence, as long as you use the same data having different parameters does not matter at all.
   **[/quote]

[jpfeifer]

The odds ratio is based on the marginal data density. That is the “likelihood” of observing the data given the model. A meaningful comparison involves keeping the data fixed and varying the model. Simultaneously changing the model and the data does not allow for a sensible comparison. Thus, the answer is no. Having Z being the sum of X and Y does not help, because the model only needs to account for this sum, not for the series individually.
To get some intuition, think about the models having k parameters and there being T observations. Then the bigger model with X and Y observed will have 2*T-k degrees of freedom while the smaller on with Z will only have T-k.

[KKLS]

Many thanks for confirming it Prof. Pfeifer,

A technical question: When I try to find the mode (given that I already have a ‘‘FILENAME_mode.mat’’)

I get a warning like this:

The steady state file internally changed the values of the following estimated parameters:

Is there a warning I should care about (indeed when I get this warning, I get a **‘‘non-positive definite Hessian matrix’’ ** problem .
Where would I look to fix that problem please ?

Ps. I googled a bit and I found a script on your github (initial_estimation_checks.m ) but it is not clear to me what the problem is in this case.